How to deform a surface 3-dimensionally with two curves
Ok, a triangle with one straight edge, two concave edges, and a concave bridge between them.
Let's start by making a triangle out of a plane like this:

Then delete only the face by selecting everything and pressing X, N.

Subdivide all three edges with 2 cuts and extrude and scale inward about this far.

Using individual origins (. for pie menu), scale the edges up until the corners are close enough to merge.

Press M and merge by distance. Increase the distance until the message at the bottom shows 3 vertices have been removed.

Select everything and fill with F.

Add a subsurf.
Holding Alt, click twice on a boundary edge to select the whole boundary. You can then set the edge creases to 1 with ShftE.
Tweak the vertices to your liking and you will get something like this:

If the normals are flipped, in edit mode, just press ShftCtrlN to calculate the normals to face opposite the &quot;normal&quot; direction (since the mesh is concave).